Elliptic curve isogeny class 900.1-m over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-900.1-m
• Conductor: 900.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 900.1-m over \(\Q(\sqrt{17}) \)

Isogeny class 900.1-m contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
900.1-m1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 186 a - 468\) , \( -2142 a + 4258\bigr] \)
900.1-m2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 34 a + 39\) , \( 59 a + 65\bigr] \)
900.1-m3	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 157 a - 400\) , \( -244 a + 624\bigr] \)
900.1-m4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -14 a - 68\) , \( -102 a - 62\bigr] \)
900.1-m5	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -623 a + 1580\) , \( -1744 a + 4476\bigr] \)
900.1-m6	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 204 a - 524\) , \( -7240 a + 18544\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph